A variational method for finite element stress recovery and error estimation

Stress recovery and error estimation for shell structures

“…Application to additional, more complex problems is required to evaluate the approach more completely. (2) In general, the use of optimal FEA stresses result in higher accuracy than non-optimal stresses (SEA OPT vs. SEA CTR ). However, in the neighbourhood of a high local stress gradient, SEA CTR performs better than SEA OPT because more data points closer to the local maximum are provided.…”

“…The smoothing element analysis was carried out in the parametric space R × ; z. Following the order-of accuracy argument discussed in Reference [2], one quadratic smoothing macro-element was used per four quadrilateral shell elements. Speciÿcally, a 3×3 mesh of smoothing elements was used.…”

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SUMMARYThe Penalized Discrete Least-Squares (PDLS) stress recovery (smoothing) technique developed for twodimensional linear elliptic problems [1][2][3] is adapted here to three-dimensional shell structures. The surfaces are restricted to those which have a 2-D parametric representation, or which can be built-up of such surfaces.

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A novel four-node quadrilateral smoothing element for stress enhancement and error estimation

“…Employing a very small β parameter (say, 10 -5 ) assures that K is nonsingular even when the minimal number of sampling stresses, N=3, is available. 17 Although this aspect permits a great range of possibilities for constructing a SEA mesh, it is highly desirable for American Institute of Aeronautics and Astronautics automation purposes that the SEA mesh be identical to the FEA mesh.…”

“…[14][15][16][17][18][19][20][21] The methodology, which is based on the minimization of a Penalized-Discrete-Least-Squares (PDLS) error functional, is highly effective and is designed to provide improved stress predictions with a higher degree of smoothness and to obtain robust a posteriori error estimates.…”